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SUMMER 2015 Volume 24 Number 2 THEORY & PRACTICE FOR FUND MANAGERS

The Education of Beta: Can Alternative Indexes Make YouAlternative Indexes Make Your r Portfolio Smarter?EUGENE PODKAMINER

THE JOURNAL OF INVESTINGSUMMER 2015

The Education of Beta: Can Alternative Indexes Make Your Portfolio Smarter?EUGENE PODKAMINER

EUGENE PODKAMINER

is senior vice president

in the Capital Markets

Research Group at Callan

Associates in San Fran-

cisco, CA.

[email protected]

Implementing a strategic asset-allocation

policy used to be straightforward: the

investor chose between active and pas-

sive approaches. Passive index tracking

provided broad exposure to a market, a fully

diversif ied benchmark for performance

measurement, and passive returns with low

implementation fees. Active management

was everything else, mainly the realization

of manager skill by delivering performance

above the passive benchmark. Passive beta has

long been synonymous with capitalization-

weighted indexes (CWI), where prices and

shares outstanding determined a security’s

weight and rebalancing was nearly automatic.

Those were the good old days.

Today so-called smart beta approaches

aim to combine both passive and active ele-

ments to deliver the best of both worlds:

transparent construction, the promise of

diversif ication, and all at low cost. In this

article, we explore how such strategies are

put together, how they have performed over

the past decade and how they can be used by

investors. We also discuss observations about

their future prospects.

Our research suggests that many forms

of smart beta feature pronounced value and

small cap tilts, which account for a signifi-

cant amount of the risk and return differences

when compared to CWI. If investors desire

such tilts, they can be easily implemented

using traditional passive and active strate-

gies. The broader question remains: What

is the economic justification for such tilts to

outperform over the long term? Without a

satisfactory answer, many smart beta strate-

gies may not be a good fit for institutional

portfolios.

THE DEMAND FOR SMARTER

INDEXES

Though widely used, CWI have their

shortcomings. Securities with inf lated prices

can balloon to take up a larger and larger

share of an index, like technology stocks

during the dot-com bubble or financials prior

to the 2008 crisis. Investors who like to avoid

bubbles (wouldn’t we all) have loudly, and

often correctly, criticized traditional indexes

for promoting stocks with poor fundamentals

only to see values come crashing down after

the bubble has popped.

An increasing number of investors

have been calling for different ways of con-

structing indexes, with weights determined

by approaches as diverse as simple averages,

quality of cash f lows, or risk. These investors

see CWI as inefficient and have conviction

that they can be smarter about index construc-

tion. Some of these alternative indexes have

been around for decades, others are newer

and seek to make traditional beta smarter.

First a brief comment on naming: many

new strategies in this area are called smart

THE EDUCATION OF BETA: CAN ALTERNATIVE INDEXES MAKE YOUR PORTFOLIO SMARTER? SUMMER 2015

beta, a name we dislike because it tells you nothing

about how it is smarter than plain-old dumb beta. The

same goes for the terms strategic, scientific, advanced,

engineered, and even better beta. We refer to strate-

gies that do not use capitalization weights as alternative

indexes because they represent an alternate approach to

the norm. Many styles fall under the broad umbrella

of alternative indexes, including low volatility indexes,

equally weighted indexes, and fundamental indexes. The

category seems to be better defined by what it is not,

rather than by what it is: alternative indexes are not capi-

talization weighted. They are also more expensive than

traditional index strategies, but cheaper than traditional

active management.

WHAT WAS OLD IS NEW AGAIN

Like many financial innovations, alternative indexes

became popular in the wake of a crisis. Investor reaction

to major drawdowns, increased focus on diversification,

and bubble avoidance set the stage for strategies that

would have done better through the turmoil of 2008.

Though the monikers smart beta and alternative index are

relatively new, the design has been around for decades.

Take the Dow Jones Industrial Average (DJIA), f irst

started in 1896. It is composed of a concentrated sam-

pling of economically significant large companies. These

securities are then weighted using a lightly modified cap-

weighted formula with some constraints. In effect the

DJIA is a “smart” index, though rarely referred to as such.

Many more examples dot the landscape, including simple

GDP- and equal-weighted equity indexes. The differ-

ence today, however, is not just the marketing. Novel

construction can lead to strategies with unique traits.

Similar to the dot-com boom, when placing a lower case

i or e in front of a company’s name nearly guaranteed a

higher earnings multiple, it would seem that calling your

strategy smart beta instantly makes it more interesting

and relevant, and promises higher returns.

THE GENESIS OF BETA AND ALPHA

Beta and alpha are at the core of the alternative

index discussion. Sharpe et al. popularized the concepts

of beta and alpha through the capital asset pricing model

(CAPM), introduced in 1964 (Sharpe [1963, 1964]). By

streamlining the tenets of Markowitz’s earlier modern

portfolio theory (MPT) into a compact and tractable

framework (Markowitz [1952]), CAPM introduced

the market as a factor through a simple yet powerful

relationship:

rp – r

f = α

p + β

p(r

m – r

f ) + e

p

Translation: a portfolio’s return is comprised

of alpha (the portion of return not explained by the

market), plus the return of the market multiplied by a

beta term.1 Under this construct the market has been

traditionally defined as a capitalization-weighted index.

Over time, the word “beta” has come to be synonymous

with the return of the market.

Sharpe’s CAPM approach describes the traditional

difference between beta and alpha that, until recently,

was the norm for many asset owners (Exhibit 1).

E X H I B I T 1

Defining Alpha and Beta

Source: Callan.


THE IMPORTANT DIFFERENCE BETWEEN

BETA AND ALPHA

Beta, based on the CAPM definition, is compensated

unconditionally, regardless of manager skill. This point is

important because it means that investors are inherently

compensated for taking on market risk, or beta, which can

be accessed relatively cheaply and reliably through index

funds. Active management, on the other hand, aims to

access elusive alpha, which—as Sharpe succinctly points

out in “The Arithmetic of Active Management”—is a

zero-sum game across all market participants (Sharpe

[1991]). An active investor that engages in security selec-

tion, market timing, sector rotation, and so on, in pursuit

of excess return is only compensated conditionally on

their skill. Since skill that generates alpha (or specifically,

positive alpha) is difficult to come by, it commands a

higher price in the marketplace.

THE EVOLUTION OF BETA

During the late 1970s and early 1980s, the CAPM

framework was adopted as the standard tool for mea-

suring the efficacy of active management—revealing just

how scarce positive alpha was. Meanwhile, the evolu-

tion of portfolio management tools and trading tech-

niques made the implementation of passive CWI ever

cheaper and more reliable. The combination of these

two trends led to the widespread adoption of passive

management.

Beginning in the late 1980s, Sharpe (and

many others) began to recognize that for many

active strategies a sizeable portion of the alpha

attributed to manager skill by the CAPM

could be reproduced using simple rules-based

approaches (Exhibit 2). The CAPM framework

was extended by using the arbitrage pricing

theorem (APT), which expands beta from a

single market measure to include any number

of factors (Roll and Ross [1980]). APT enables

us to think in terms of multiple betas (or fac-

tors), including style (growth and value), capi-

talization (large, mid, small), and momentum

(persistence among winners). This led to the

development of rules-based style indexes such

as the Russell 1000 Growth Index or the S&P

600 Small Cap Value Index. These indexes

represented both a more accurate way to mea-

sure the true alpha being generated by a strategy, and

a cheaper way to passively access the persistent factor

exposures inherent in a strategy.

Conceptually, many smart beta strategies are really

no different from the original style indexes. Though

each of these newer strategies may emphasize a different

set of market exposures, they all use fairly transparent

rules-based approaches to efficiently and cheaply imple-

ment a combination of factors. The challenge for inves-

tors is in deciding which factors to emphasize (if any),

and to implement them consistently across a complex

multi-asset class portfolio.

BUILDING BETA: THREE DECISIONS

FOR INDEX CONSTRUCTION

Building an index, whether smart, cap-weighted,

or otherwise, relies on three important decisions: 1)

defining the investable universe (for example, emerging

market small cap or U.S. broad cap); 2) determining

the weighting scheme; and 3) specifying constraints (for

example, maximum position sizes or liquidity param-

eters). Alternative indexes tend to differ from traditional

CWI on all three levels (Amenc et al. [2012]). Exhibit 3

presents a hierarchy for index construction and separates

the weighting decision into three schemes:

a. Simple reweighting includes equal weightings

across securities, countries, or regions/geographies;

equal contribution to risk; and GDP weighting.

E X H I B I T 2

The Evolution of Alpha and Beta

Source: Callan.


b. Risk-aware weighting focuses on the contribution

to portfolio risk and can result in risk-weighted,

minimum/low volatility/variance, as well as max-

imum Sharpe ratio portfolios (which use both risk

and return).

c. Return-aware weighting focuses on some com-

bination of fundamental factors such as value,

dividend, momentum, and quality, which are

presumed to have a persistent positive inf luence

on return.

Before proceeding to alternative indexes, we

brief ly explore how three common cap-weighted equity

indiexes are constructed: the S&P 500, Russell 3000,

and MSCI EAFE.

• The S&P 500’s universe selection includes “500 of

the top companies in leading industries of the U.S.

economy” with market capitalizations of more

than $4.6 billion (as of March 31, 2014), and with

at least 50% of the shares outstanding available for

trading. The inclusion criteria are carefully man-

aged by committee and therefore do not simply

represent the largest 500 companies. Constituent

stocks are weighted based on market capitalization

and constraints, including positive earnings over

recent periods and adequate liquidity.2

• The Russell 3000 is more transparent in construc-

tion, as the universe selection consists of all U.S.

common stocks. These are ranked annually from

largest to smallest market capitalization, and the

top 3,000 stocks form the Russell 3000 Index.

Constraints exclude stocks that trade for less than

$1.00, stocks with market capitalizations under $30

million, and foreign stocks.3

• The MSCI EAFE (Europe, Australasia, and Far

East) selects the largest 85% of stocks from each of

21 developed market countries, weighted by free-

E X H I B I T 3

Build an Index in Three Easy Steps

Source: Callan.


f loat adjusted market capitalization (which includes

only shares readily available in the market), with

typical liquidity and investability constraints

applied.4

Build Your Own Index

In the cap-weighted examples above, the uni-

verse selection alone can provide a portfolio bias toward

some characteristics (as in the S&P 500), whereas the

weighting scheme determines how individual securities

are combined. Some alternative indexes are specified

entirely at the universe selection level. For instance, the

allowable universe can be defined as low volatility stocks

(those with lower historical standard deviations), but the

weighting scheme may be cap weights. Typically alterna-

tive indexes both redefine the universe and employ an

alternative weighting scheme. A low volatility index may

use the same starting point as the example above, but

can weight those low volatility securities in a risk-mini-

mizing manner to create a minimum variance portfolio.

Multiple approaches can be combined, and the process

can be applied to equity or fixed income securities.

The Limits of Diversification

Many alternative index approaches introduce

tilts when compared to traditional CWI, such as over-

weighting value or small cap stocks. These factor

tilts seem incidental at first. They are rarely obvious

when learning about how a particular strategy is

built, but they are crucial to our understanding of

how alternative indexes differ from CWI. Just like

traditional CWI, alternative indexes focus on a

single asset class, equities most often, and are long

only (no shorting is allowed). Although alterna-

tive indexes can be found in several asset classes,

we focus our analysis exclusively on U.S. equity

strategies.

Exhibit 4 illustrates the distinction between

alternative indexes and multi-asset class strategies,

such as risk factor, risk premia, or risk parity, many

of which use shorting. This distinction is important

because if you desire to isolate a particular factor

(for example, value), then doing so across several

asset classes with the ability to short is surely more

efficient than limiting a strategy to a single asset

class and prohibiting short selling (Grinold and Kahn

[2000]).

And therein lies the rub. Smart beta strategies are

often marketed as good diversifiers or volatility reducers.

But if the index is composed of the same securities as

a CWI (for example, large cap U.S. stocks), then no

matter how much you reweight the names, a very high

degree of correlation remains. The same goes for vola-

tility. Certainly, some low volatility strategies have lower

risk, but there is no reason to expect that a different

weighting scheme will magically result in an overall

public equity portfolio that is appreciably less risky.

The three most popular types of alternative indexes

are low volatility, fundamental, and equally weighted.

We take a closer look at each to better understand what

benefits these strategies deliver, how they can be used

within a portfolio, and the assumptions on which they

are based.

Low Volatility Indexes

The promise of low volatility strategies is to reduce

the total risk (as measured by standard deviation)—as

opposed to active risk—of the index by carefully selecting

less risky stocks. This, in aggregate, is designed to result

in a more efficient portfolio with returns similar to the

overall market. Low volatility stocks can have a value

bias because dull companies that do not grab headlines

E X H I B I T 4

Examples of Alternative Indexes and Other Strategies

Source: Callan.


tend to be less volatile than the hot technology firm

that just released the new must-have mobile device or

the pharmaceutical company that just obtained FDA

approval for a drug. We often hear behavioral finance

arguments put forth for why low volatility strategies will

continue to outperform CWI: irrational investors shun

lower-risk stocks (and overpay for higher-risk stocks),

classic return-chasing behavior by emotional investors,

and asset managers focusing on information ratios rather

than Sharpe ratios. Not all market participants believe

that these behaviors will persist.

Low volatility strategies represent a number of

approaches that include minimum volatility, minimum

variance, and maximum Sharpe ratio (MSR). Though

these terms sound somewhat similar, there are big dif-

ferences in the way each strategy is assembled. There

are three main approaches to putting together such an

index. The first involves just picking from a set of low

volatility stocks and using capitalization weights. The

second expands on this by using optimization tools to

weight the low volatility stocks into a low volatility

portfolio. The third approach is to select from low and

high volatility stocks and optimize them into a portfolio

with the best return/risk ratio (as represented by the

Sharpe ratio). The subtleties are important because each

approach leads to a unique portfolio.

The MSCI USA Minimum Volatility Index uses the

MSCI USA as a starting point and optimizes the stocks

for the lowest absolute volatility (subject to constraints

which help maintain investability). On the surface, the

strategy seems to meet the stated goals: over the past

10 years ending December 31, 2013, performance has

exceeded the S&P 500 by 0.85% whereas realized stan-

dard deviation has been lower (11.66% versus 14.69%).

However, over the past five years ending December 31,

2013, performance has lagged the CWI S&P 500 by

1.56%. Tracking error, when compared to the S&P 500,

has been similar to many traditional active managers, in

the 5% to 7% range—a far cry from the 0% expected of

cap-weighted index-tracking funds.

We use a Sharpe returns-based style analysis to plot

the footprints of the strategy over the past 10 years (using

rolling three-year periods) in Exhibit 5 (Sharpe [1992]).

For comparison and reference, we include the standard

MSCI USA Index. We observe two biases: an overweight

to smaller cap stocks (especially between 2003 and 2008)

and a pronounced value tilt (darker-shaded bars). The

choppiness observed in the low volatility analysis is

due to frequent required rebalancing, a hallmark of all

alternative index strategies. The MSCI USA Minimum

Volatility Index annual turnover is constrained to a

maximum of 20% as compared to a realized turnover

of 2.5% for the cap-weighted MSCI USA.5

The R2 measure, which can range from 0 to 1,

indicates the proportion of variation in the returns that

is explained by the characterization in the style analysis.

The minimum volatility index’s R2 is nearly 0.75, which

implies a moderately strong relationship: something

other than simply reweighting slices of CWI is respon-

sible for the return pattern. For reference, the MSCI

USA Index R2 is 0.99.

In Exhibit 6, we use a style map to offer another

perspective on the difference that index construction

choices make between the minimum volatility index (in

orange) and the MSCI USA Index (in teal). The ovals

for each index represent roughly 80% of the observations

and provide an indication of drift. Whereas the MSCI

USA Index is very close to the S&P 500 (both are large

cap and style neutral), the minimum volatility index is

skewed to value and lower capitalization stocks. These

two factor tilts (small cap and value) are observed in

other low volatility indexes as well.

But what about diversif ication? Does adding a

minimum volatility strategy reduce the overall equity

portfolio’s risk? Over the past 10 years ending December

31, 2013, this strategy has exhibited a 0.93 correlation

with the S&P 500. Despite lower risk than cap-weighted

indexes, it is still highly correlated with them. (See

Appendix A for correlations with a range of standard

indexes and excess correlations against other alternative

index strategies.)

FUNDAMENTAL INDEXES

Fundamental indexes shun market capitalization as

the appropriate measure of economic size, and instead

focus on various alternative measures including sales

revenue, cash f low, dividends, and stock buybacks. The

Russell Fundamental U.S. Index uses all three of these

alternative measures (Russell partners with Research

Aff iliates to develop the Index). Using sales f igures

adjusted for leverage minimizes heavily leveraged com-

panies; operating cash f low is a proxy for balance sheet

health; and dividends plus stock buybacks ref lects on

overall enterprise health and management confidence.

The goal of such strategies is to take advantage of the


E X H I B I T 5

MSCI USA Minimum Volatility and MSCI USA Style Analyses

(monthly data for 10 years ending 12/31/2013, rolling 36-month periods)

Sources: Callan, MSCI.

E X H I B I T 6

MSCI USA Minimum Volatility Index Style Map


Sources: Callan, MSCI, Russell, Standard & Poor’s.


disconnections between share prices and other funda-

mental metrics of company success.

The style analysis footprints of the fundamental

index point out a strong value bias (nearly all of the bars

are darker shades) and a tilt toward smaller cap stocks,

as seen in Exhibit 7. Unlike the previous low volatility

example, the style analysis R2 is high (0.9896), which

implies that we could recreate this index by using a

combination of cap-weighted passive (or active) port-

folios. The Russell Fundamental U.S. Index’s annual

turnover is expected to be between 10% and 12% (Hsu

and Campollo [2006]). For reference we include the

standard Russell 3000 Index style analysis.

This fundamental index has outperformed the

S&P 500 by 2.65% over 10 years ending December

31, 2013, but with moderately more volatility (15.98%

versus 14.69%). Tracking error is nearly 3% over this

period. Over the past five years, we find that perfor-

mance, total risk, and tracking error are each higher.

Tracking error for the fundamental index is lower than

the minimum volatility index because the strategy hews

closer to the cap-weighted benchmark, as seen by the

higher R2 and somewhat smoother style analysis. In

the total risk dimension (as opposed to tracking error),

the minimum volatility index is lower than the funda-

mental index (11.66% versus 15.98% for 10 years ending

December 31, 2013).

Exhibit 8 illustrates characteristics of the Rus-

sell Fundamental U.S. Index using a style map. The

pronounced value bias and small capitalization tilt are

readily apparent. Similar to the low volatility index,

the correlation with the S&P 500 is very high (0.9860),

limiting the benefit of diversification.

E X H I B I T 7

Russell Fundamental U.S. and Russell 3000 Style Analyses


Sources: Callan, Russell.


EQUALLY WEIGHTED INDEXES

Equal weighting is the simplest form of index con-

struction. In light of the more complex approaches dis-

cussed earlier, averaging an entire universe eliminates

many complicated choices. One well-known example

is the S&P 500 Equal Weight Index, which consists of

the same constituents as the widely tracked S&P 500,

but with each company allocated a fixed 0.2% weight.

Intuitively, we know that such a weighting scheme will

introduce a significant small cap bias because the stocks

that have a lower market capitalization are now held at

the same weight as major multinational corporations.

We expect that the portfolio will likely also have a value

tilt because equal weighting will expand the presence

of value stocks, which tend to trade at lower multi-

ples. Equal weighting is widely used in active manage-

ment, where, for instance, a fundamental manager will

equally weight 30 high-conviction stocks to form her

portfolio.

The style analysis in Exhibit 9 confirms both of

these exposures. Notice the scarcity of large cap (green

bars) and the prevalence of value (dark shading). The

R2 of the equally weighted index is 0.9827, which

means that the vast majority of the variation in returns

is explained by the style analysis characterization. For 10

years ending in 2012, the average annual turnover for

the equal-weight index was 24.7%, much higher than

the S&P 500’s turnover of 6.3% (Zeng and

Luo [2013]). For comparison we include the

standard S&P 500 Index style analysis.

The style map in Exhibit 10 illustrates

the relative magnitude of the value and small

cap tilts, both of which are pronounced.

As with the two previous examples,

performance relative to the S&P 500 has

been strong over the past 10 years ending

December 31, 2013, with the equal-weight

index beating the cap-weighted bench-

mark by 2.38%. However, historical risk

over this period was much higher, 17.61%

versus 14.69% for the S&P 500. Similarly,

tracking error is near 5%. This index relies

on the same stocks as in the S&P 500, so we

expect a very high correlation with the cap-

weighted index. Over the 10-year period

ending December 31, 2013, the correlation

is 0.9743. Looking forward, we have a hard

time developing an economic justif ication

for why equal weighting a portfolio should deliver out-

sized returns.

All three alternative index strategies seem to exhibit

positive performance versus cap-weighted benchmarks.

This could be for a variety of reasons, including the

use of data mining in the development of these strate-

gies. Value and small cap were rewarded over the past

10 years; the amount of readily available data does not

include many periods where these strategies underper-

form. Factor tilts are prevalent in alternative indexes and

have certainly paid off recently—but is it reasonable to

assume that they will do so going forward? (Amenc and

Martellini [2014]).

Interested readers can examine findings from eight

additional alternative indexes covering U.S. and non-

U.S. equity in Appendix A. Results are broadly similar

across all strategy types.

ALTERNATIVE INDEXES: ACTIVE

OR PASSIVE?

Does a mechanical, rules-based strategy meet the

definition of active management? A strong argument

can be made that any weighting scheme or security-

selection process other than cap-weighted is active. For

a real world illustration we turn to low-risk active or

E X H I B I T 8

Russell Fundamental U.S. Index Style Map


Sources: Callan, Russell, Standard & Poor’s.


enhanced indexing strategies popularized

in the 1990s by quantitatively oriented asset

managers. These strategies start with a CWI,

and then carefully reweight the compo-

nent stocks or bonds within tightly defined

parameters while adhering to industry and

sector neutrality.

Enhanced index strategies were pre-

sented to investors as lower-fee, quasi-

passive products, but were then typically

categorized as active strategies because the

portfolio manager’s judgment could effec-

tively override model weights. The primary

difference between alternative and enhanced

index strategies has to do with where deci-

sions are made in the hierarchy of portfolio

management events—in universe selection

and weighting schemes for alternative index

E X H I B I T 9

S&P 500 Equal Weight and S&P 500 Style Analyses


Sources: Callan, Standard & Poor’s.

E X H I B I T 1 0

S&P 500 Equal Weight Index Style Map




strategies, and in security selection for enhanced index

products (given that the universe selection is the same

as the underlying benchmark and differences between

benchmark capitalization weighting and enhanced port-

folios are relatively small). Another big difference is that

enhanced index strategies are tuned to minimize tracking

error relative to a traditional CWI, whereas alternative

indexes are constructed without tracking error in mind.

Selecting a tilt is itself an act of judgment, and renders

the resulting alternative index strategy active. The deci-

sion to include an alternative index strategy in a port-

folio is an active one, even if the implementation of the

strategy is mainly passive. The investor is making an

active choice, akin to the decision that an asset manager

makes when tilting a portfolio toward a certain factor,

security, sector, or region.

Like active management, if all market participants

adopted alternative index strategies, the average of their

investments would still aggregate to traditional CWI

definitions. This process feeds back into setting prices

and informs CWI weights. Alternative indexes aggre-

gate to a zero-sum game.

WHERE DO ALTERNATIVE INDEX

STRATEGIES FIT IN THE PORTFOLIO?

Alternative index strategies are typically single asset

class and long only, and are relatively easy to place within

the corresponding equity or fixed income sleeve. Some

investors may want to include alternative index strategies

in their hedge fund or alternatives allocations. However,

should capital for alternative index strategies be sourced

from existing active or passive CWI allocations? The

answer may depend on how skeptical the investor is of

traditional active management. Allocating to lower-fee,

transparent, and mechanical alternative index strategies

may make sense for investors who grudgingly engage in

active management. On the other hand, investors who

are convinced of the merit of active management may

wish to exchange traditional index holdings for alter-

native index strategies (resulting in additional tracking

error). We have observed alternative index strategies

used in the following ways:

• Low/minimum volatility strategies coupled with

liability-driven investing (LDI) portfolios promise

low surplus risk6 for investors who are hedging

liabilities.

• Low/minimum volatility strategies, used when an

investor is required to hold a high equity alloca-

tion, aim to reduce overall portfolio risk.

• Fundamental index strategies can be a substitute for

CWI if the investor believes they are more repre-

sentative of the market, or as a substitute for active

managers for active-management nonbelievers.

• Equally weighted approaches intentionally lower

portfolio capitalization, which offers liquidity to

the small cap market.

All alternative index strategies strive to deliver a

return stream different from traditional strategies, but as

previously noted, their diversification has limits.

Characteristics When Added to a Portfolio

To see how alternative indexes interact with the

other portfolio components, we show the risk-and-re-

turn effects of adding a 15% allocation to each of the

three alternative indexes analyzed in detail; this alloca-

tion is carved out of the U.S. equity cap-weighted Rus-

sell 3000 Index in Exhibit 11. We begin with a reference

portfolio made up of 30% U.S. equity (Russell 3000),

30% developed ex-U.S. equity (MSCI EAFE), and 40%

U.S. investment-grade bonds (Barclays Aggregate). For

the 10 years ending December 31, 2013, the reference

mix returned 6.65% (with 9.95% standard deviation).

Mixes 1, 2, and 3 each add 15% to a single alter-

native index strategy (MSCI USA Minimum Volatility

Index, Russell Fundamental U.S. Index, and S&P 500

Equal Weight Index, respectively). All three mixes

achieved higher return than the reference portfolio, but

Mix 2 and Mix 3 did so by assuming more risk, whereas

Mix 1 (with the minimum volatility index) somewhat

lowered portfolio risk. Detailed characteristics for each

strategy can be found in Appendix A.

This backward-looking analysis suggests that

adding moderate amounts of alternative index strate-

gies to a standard-reference portfolio slightly improves

risk-adjusted return characteristics. Whether these rela-

tionships persist going forward is the obvious question

for asset owners. To assert a return premium or risk

advantage over CWI, we must believe that the universe-

selection and weighting-scheme decisions offer an eco-

nomic or behavioral rationale for better returns.

As a counterpoint to the f irst three mixes, we

construct Mix 4 by excluding all alternative indexes


and instead adding 5% to fixed income sourced from

global equity (Exhibit 12). Intuitively, we expect the

total portfolio’s historical return to decrease, and it does

so by 0.14% (from the reference mix’s 6.65% to 6.51%

over the past 10 years). However, 10-year historical risk

falls by more than 0.76% (from 9.95% to 9.18%). If the

investor’s objective is to reduce risk and increase the

return/risk ratio, then adding bonds to an equity-heavy

portfolio historically provides more powerful results

than changing the mix of equity strategies to include

alternative indexes. Note that fixed income may offer

a different forward-looking risk-adjusted return profile

than we have historically observed. This point bears

repeating: The market consensus points to weak fixed

income returns over the next several years. Forward-

looking asset allocation decisions require appropriate

forward-looking views.

ASSET OWNERS AS ASSET MANAGERS

Many institutional asset owners already engage

in a big-picture form of smart beta by biasing portfo-

lios toward small cap, value, their home country, and

emerging markets. Using traditional active managers,

the investor typically specifies the universe (for example,

emerging-market debt or global developed equity) and

the manager is responsible for security selection or

weighting (Exhibit 3). By contrast, with an alterna-

tive index strategy, these decisions are shifted to the

asset owner. This shift on a policy level, from CWI to

alternative indexes, moves some of the asset-manage-

ment burden to the asset owner because they are now

responsible for security selection and other basic strategy

definitions. Those investors allocating to alternative

index strategies should have appropriate governance and

benchmarking policies in place.

E X H I B I T 1 2

Changing the Asset Allocation

(data for 10 years ending 12/31/2013)

Source: Callan.

E X H I B I T 11

Adding Alternative Indexes to the Portfolio

(data for 10 years ending 12/31/2013)

Source: Callan.


CONCLUSION

This article explores the origins of alternative

indexes, how their construction reveals specific factor

tilts, and their impact when paired with traditional

cap-weighted indexes in a portfolio. Examining three

alternative index strategies in detail, we found that they

feature significant exposure to value and small cap, which

may not be rewarded in the future, though historical

performance has been favorable. The various tilts found

in alternative index strategies are obscured by naming

conventions and marketing, but are readily apparent

upon empirical examination. Interested readers can find

additional analysis (including a Fama–French–Carhart

regression) on 11 alternative indexes in Appendix A.

Alternative indexes are one way to express a belief

in value and small cap factor tilts. Investors already use

traditional value and small cap strategies (active and

passive) to tilt portfolios toward these factors. For an

investor who really believes in value and small cap (or

other factors), the most efficient way to implement is

by adopting a risk-premia strategy that can invest across

multiple asset classes and permits short selling, which is

far more compelling than a single-asset-class, long-only

alternative index strategy (Podkaminer [2013]). Addi-

tionally, alternative indexes appear to offer minimal

diversification benefits versus traditional cap-weighted

indexes: Rearranging stocks picked from the same pool

still leads to very high correlations.

Investors who are skeptical of active management

can use alternative indexes to extend a passive core to

obtain exposure to desirable factors in a transparent

manner. On the other hand, investors who believe in the

value of active management can use alternative indexes

to obtain low-cost, semipassive exposure in a portfolio

dominated by traditional active strategies. Regardless

of your perspective, the availability of a middle-ground

option located between active and passive enables greater

control in constructing portfolios of managers when

implementing a strategic asset allocation.

A P P E N D I X A

We expand on the three alternative index analyses pre-

sented earlier to include an additional eight strategies.

Empirical analysis provides intuition about the per-

formance and risk differences between cap-weighted and

alternative indexes. However, the time period examined

substantially impacts the results. Data for many alternative

indexes are available only in back-test form, and even then the

history tends to be brief by statistical standards. The dearth

of data coupled with the unusual period suggests placing

less emphasis on historical empirical results versus forward-

looking expectations. Additionally, the wide-scale adoption

of factors and tilts is a relatively new phenomenon, which is

not captured in the back-test period.

Our analysis includes 11 alternative equity indexes (six

U.S. shaded in green and five developed ex-U.S. shaded in

orange). Each index is picked for its unique construction,

which is based on various choices for universe selection,

weighting scheme, and constraints (Exhibit A1).

MSCI: The minimum volatility indexes strive to

ref lect the performance characteristics of a minimum vari-

ance strategy by optimizing the parent index (MSCI USA and

MSCI EAFE in this analysis) for the lowest absolute volatility

for a given covariance matrix of stock returns within a set of

constraints that maintain index replicability and investability.

Constraints include turnover limits along with minimum and

maximum constituent allocations and sector and country

weights relative to the parent index. The index is rebalanced

(or reoptimized) semiannually.

S&P: The equal-weight index consists of the same con-

stituents as the widely tracked S&P 500, but each company is

allocated a fixed weight (0.2%) and is rebalanced quarterly.

Russell/Research Affiliates: The index starts with

the Russell Global Index universe with a liquidity screen

applied that captures 95% of liquidity based on average daily

dollar-traded volume to facilitate investability. Three mea-

sures of economic size are selected: adjusted sales, retained

operating cash f low, and dividend plus buybacks, all averaged

over five years. Securities representing the bottom 2% of the

fundamental weight are removed to enhance investability.

FTSE RAFI: The index comprises 1,000 companies

with the largest RAFI fundamental scores selected from the

corresponding FTSE parent indexes. The scores are based on

four fundamental factors: dividends, cash f lows, sales, and

book value. Screens are applied for liquidity, and the index

is reviewed annually.

ERI: The maximum deconcentration strategy aims to

maximize the effective number of stocks, which is equivalent

to minimizing the concentration as measured by the Her-

findahl Index. This strategy aims to get as close as possible

to equal weights while respecting practical investment con-

straints, including turnover and liquidity concerns. The max-

imum decorrelation strategies combine securities specifically

to exploit the risk-reduction effect stemming from low cor-

relations (instead of reducing portfolio risk by concentrating

in low volatility stocks). For high-liquidity indexes, only

the most liquid constituents are selected (those with a score


above the 60th percentile). Index turnover is constrained and

liquidity adjustments are made. The indexes are reviewed in

full annually and are reoptimized at least biannually.

Our analysis shows that alternative index weighting

schemes can lead to significant exposure to equity risk factors,

even in those cases where the strategy objective does not specify

a factor tilt. We calculate empirical results using two methods:

(1) returns-based style analysis with index-based factors and (2)

Fama–French–Carhart four-factor regression for U.S.-based

strategies and four-ratio regression for developed ex-U.S. strat-

egies (Fama and French [1993] and Carhart [1997]).

Index-Based Factor Analysis

Exhibit A2 shows the performance of six style indexes

for the past 20 years in a periodic table format. We segment

the U.S. market universe by capitalization and style with the

Russell Top 200 (green), Mid Cap 800 (blue), and Small Cap

2000 (yellow), Growth (lighter shades) and Value (darker

shades) indexes. These six components enable us to explore

the various size and capitalization characteristics of alternative

index portfolios. There is little persistence in the ranking of

each component over time, which acknowledges that skill is

necessary to select top-performing components: a systematic

tilt to a particular component does not guarantee superior

long-term returns.

In Exhibit A3, we look at the six U.S. alternative indexes

in a Sharpe returns-based style analysis (simply a regression

constrained to sum to 100%) to effectively model capital-

ization and style loadings. Each analysis covers 13 years of

monthly data, starting January 1, 2000, and uses rolling three-

year periods (ERI Index inception is mid-2002, so 11.5 years

of data are available for the style analysis). The plots repre-

sent the performance footprints of each strategy and illustrate

the relatively active nature of the alternative index strategies

versus a traditional CWI and uncover portfolio tilts.

E X H I B I T A 1

Alternative Index Characteristics

Sources: Callan, ERI, FTSE, MSCI, Russell, Standard & Poor’s.

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E X H I B I T A2

U.S. Equity Capitalization and Style Index Performance

(20 years ending 12/31/2013)

Sources: Callan, Russell.


E X H I B I T A3

U.S. Alternative Index Style Analyses




E X H I B I T A4

U.S. Reference Index Style Analyses



E X H I B I T A5

U.S. Style Map




Of note are the capitalization differences

between the alternative index strategies and the

cap-weighted S&P 500 and Russell 3000 reference

indexes shown in Exhibit A3. The MSCI USA Min-

imum Volatility strategy appears to have loaded up

almost exclusively on mega cap stocks since 2008

and has a value bias. The ERI SB U.S. Low Vola-

tility Maximum Deconcentration strategy exhibits

similar behavior but demonstrates more mid cap

value loading. The S&P Equal Weight Index fea-

tures a high allocation to mid cap, particularly mid

cap value, with large cap value rounding out the

mix. Both the Russell Fundamental U.S. and the

FTSE RAFI U.S. 1000 Indexes are heavily value

tilted, with significant exposure to both large and

mid cap value. The ERI SB U.S. High Liquidity

Maximum Decorrelation strategy is growth biased

and overweight to mid cap versus the cap-weighted

market indexes. Each of these tilts will help inform

the risk and return characteristics examined in the

next section.

With the exception of the MSCI USA Min-

imum Volatility strategy, the R2 (a measure of the

goodness of fit) for these constrained regressions is

very high (0.98 or higher), with 0.9896 for the Rus-

sell Fundamental U.S. Index. The vast majority of

factor tilts appear to be captured by style.

For comparison, we analyze the CWI bench-

marks in Exhibit A4, revealing relatively static expo-

sure to capitalization and style when compared to

the alternative index strategies. As expected, the R2

for the S&P 500 and Russell 3000 are 0.9992 and

0.9999, respectively.

These characteristics are summarized in the

style map in Exhibit A5, which plots each alternative

index strategy and reference CWI on capitalization

and style axes. The ellipses cover 80% of the data

and provide an idea of dispersion over time. Not

surprisingly, given the significant value and size tilts

observed earlier, most of the alternative index strate-

gies tend to skew toward value and exhibit markedly

smaller capitalizations than the S&P 500 or Russell

3000. The most heavily value-oriented strategy of

the six is the FTSE RAFI U.S. 1000, whereas the

ERI SB U.S. High Liquidity Maximum Decorrela-

tion is skewed to growth.

We run a similar analysis for the developed

ex-U.S. market as def ined by the MSCI EAFE

Index. The universe is broken up into four seg-

ments based on style and region: Europe growth and

value (teal), and Pacific growth and value (orange).

Exhibit A6 shows the performance of these four EX

HI

BI

T A

6

No

n-U

.S. E

qu

ity

Sty

le I

nd

ex P

erf

orm

an

ce

(20 y

ear

s en

din

g 1

2/3

1/2013)

Sou

rces

: C

alla

n,

MSC

I.


E X H I B I T A7

Non-U.S. Alternative Index Style Analyses


Sources: Callan, ERI, FTSE, MSCI, Russell.


components for the past 20 years. As with the U.S. analysis,

there is little persistence in the ranking of each component

over time.

Exhibit A7 shows the Sharpe returns-based style analysis

approach used to model regional and style loadings for the five

developed ex-U.S. alternative index strategies. Correspond-

ingly, each analysis covers 13 years of monthly data, starting

January 1, 2000, and uses rolling three-year periods (MSCI

EAFE Minimum Volatility inception is December 2001, so

just over 12 years of data are available for this analysis; ERI

index inception is mid-2002, so 11.5 years of data are avail-

able for this analysis).

The style analyses feature high R2 figures, most above

0.92, which indicate very robust explanatory power. Analo-

gous to the U.S. analysis, the MSCI EAFE Minimum Vola-

tility R2 is lower than the rest of the group, at 0.78. Many of

the plots feature a high allocation to value factors, consistent

with the strategy-construction methodology. For reference,

the MSCI EAFE Index is shown in Exhibit A8; the R2 is

0.9999.

E X H I B I T A8

MSCI EAFE Reference Index Style Analysis


Sources: Callan, MSCI.

E X H I B I T A9

U.S. Fama–French–Carhart Regression

(monthly data for 10 years ending 12/31/2013)

Sources: Callan, ERI, FTSE, MSCI, Russell, Standard & Poor’s, Kenneth French Data Library, http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.


Regression-Based Factor Analysis

To corroborate the style analysis above, we also per-

form linear regression on the U.S.-based strategies using the

well-known Fama–French–Carhart factor model constructed

using six value-weighted portfolios based on size, book-to-

market, and momentum. Factors include:

• excess market return (Mkt-Rf ): value-weighted return

of all CRSP firms incorporated in the U.S. and listed on

the NYSE, AMEX, or NASDAQ that have good data

minus the Treasury-bill rate from Ibbotson Associates

• small minus big (SMB): the average return on the three

small cap portfolios minus the average return on the

three large cap portfolios

• high minus low (HML): the average return on the two

value portfolios minus the average return on the two

growth portfolios

• momentum (MOM): the intersection of two portfolios

formed on size and three portfolios formed on prior

return: ½ (small high + big high) – ½ (small low +

big low).

For the developed ex-U.S. market, we use four factor

families grouped into several buckets, each with countries

represented by the MSCI EAFE universe. These factors

include:

• book-to-market (B/M)

• earnings-to-price (E/P)

• cash earnings-to-price (CE/P)

• dividend yield (D/P).

Within each factor the stratification is as follows:

• value portfolio high contains firms in the top 30% of a

ratio

• growth portfolio low contains firms in the bottom 30%

of a ratio.

The factor-based analysis is largely consistent with our

previous index-based analysis. Exhibits A9 and A10 present a

summary of regression results. We find that the R2 terms are

proportionally similar to the earlier analysis, with the MSCI

EAFE Minimum Volatility Index generating the lowest R2

(at 0.66), and all the remaining strategies’ R2 above 0.94.

Factor loadings with t-statistics greater than a ±2 threshold

are shaded. Note that all six strategies load significantly on the

excess market return (Mkt − Rf ) with t-statistics above 13.

This result will also be corroborated in the subsequent cor-

relation analysis.

Three of the U.S. alternative index strategies exhibit a

pronounced small cap bias (MSCI USA Minimum Volatility,

S&P 500 Equal Weight, and Russell Fundamental U.S.). This

should come as no surprise, since the equal-weighted index

construction criteria and the Russell Fundamental U.S. Index

style analysis also support this finding.

E X H I B I T A10

Non-U.S. Four-Factor Regression


MSCI EAFE Min Vol Dev. LC

Sources: Callan, ERI, FTSE, MSCI, Russell, Standard & Poor’s, Kenneth French Data Library, http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.


E X H I B I T A11

Periodic Tables of U.S. and Non-U.S. Alternative Indexes and Cap-Weighted Benchmarks

(nine years ending 12/31/2013)



Value orientations are apparent in nearly all U.S. port-

folios (S&P 500 Equal Weight, Russell Fundamental U.S.,

FTSE RAFI U.S. 1000, and ERI SB U.S. Low Volatility

Maximum Deconcentration), with t-statistics largely cor-

roborating value exposure observed in the style analysis.

The ERI SB U.S. High Liquidity Maximum Decorrelation

portfolio has a negative weight to value because it is a growth-

tilted portfolio by construction. Generally, the momentum

factor is muted, likely as a result of rebalancing parameters,

with statistically significant negative exposure for the S&P

500 Equal Weight, Russell Fundamental U.S., and FTSE

RAFI U.S. 1000 strategies.

The developed ex-U.S. framework is somewhat dif-

ferent than the U.S.-based analysis but still provides useful

insight. We observe that all of the R2 terms are very high

(over 0.94), providing some statistical comfort in the findings.

With the exception of the Russell Fundamental Developed

Large Cap strategy, all portfolios had statistically significant

positive weights to the B/M factor (and three, including the

Russell Fundamental Developed Large Cap, to the High B/M

slice). Both the MSCI EAFE Minimum Volatility and FTSE

RAFI Developed 1000 show positive weights to higher-

yielding stocks.

Overall, the high R2 terms and signif icant factor

weights provide compelling evidence that these alternative

index portfolios are constructed with meaningful tilts that

contribute to risk and return characteristics.

Return and Risk

Analysis of total returns show that many of the alter-

native index strategies outperformed their respective CWI

counterparts over the past 10 years (through December 31,

2013). Exhibit A11 illustrates returns in a periodic table

format for the past nine calendar years. Excess returns cal-

culations versus the S&P 500 and MSCI EAFE benchmarks

more clearly present each strategy’s unique performance (see

Exhibit A12).

E X H I B I T A12

Summary Performance and Risk Statistics




Turning to risk, we observe that some alternative index

strategies had markedly higher annualized standard deviation

than the S&P 500 over the same time period. Both low vola-

tility strategies did indeed exhibit lower volatility. Tracking

error for U.S. strategies versus the S&P 500 is in a similar

range to many traditional active strategies, 3% to 5%. Tracking

error for developed ex-U.S. alternative index strategies versus

MSCI EAFE is higher than their U.S. counterparts, with some

over 7%. Note that tracking error may not be as applicable to

alternative index strategies as with traditional active strategies

because these portfolios are constructed without reference to

the cap-weighted benchmark, but nevertheless will be used

by many investors for attribution and performance measure-

ment purposes. Looking at overall standard deviation is likely

a more relevant calculation. Information ratios do vary over

time, but are robust over the 10-year sample (Exhibit A12).

E X H I B I T A13

Cumulative Performance


Sources: Callan, ERI, FTSE, MSCI, Russell, Standard & Poor’s

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E X H I B I T A14

Historical Total Return Correlations for Alternative and Cap-Weighted Indexes

(10 years ending 12/31/2013)

Sources: Callan, Barclays, ERI, FTSE, MSCI, Russell, Standard & Poor’s


Over 10 years, Sharpe ratios ref lect stronger risk-

adjusted performance for alternative index strategies (0.45

to 0.62 versus 0.39 and 0.43 for the S&P 500 and S&P 500

Growth, respectively). The developed ex-U.S. strategies have

a wider distribution of Sharpe ratios, from 0.24 to 0.58 as

compared to 0.29 for the MSCI EAFE. Though alternative

indexes have performed well in the past (and especially over

this 10-year sample), their historical performance is no indi-

cator of future outperformance (Exhibit A13).

Correlation Analysis

Though alternative indexes promise diversif ication,

our analysis concludes the opposite: correlation is very high

with traditional cap-weighted indexes. We find that alterna-

tive index strategies are highly correlated with broad equity

markets over multiple time periods. Because the universes are

the same for alternative indexes and cap-weighted indexes

(and both prohibit shorting), it is no surprise that most are

greater than 0.96 correlated with the S&P 500. Of this group,

both MSCI minimum volatility strategies have the lowest

correlations, which have been trending downward since

mid-2011. Exhibit A14 shows correlations over the 10-year

period ending December 31, 2013. Interestingly, the alter-

native indexes are themselves highly correlated (0.9481 for

U.S.-based strategies over 10 years and 0.9428 for developed

ex-U.S. strategies, on average).

When we examine excess correlations (versus the S&P

500 and the MSCI EAFE, respectively), we can directly

observe the relationship among the factor tilts (Exhibits A15

and A16). As expected, the MSCI USA Minimum Vola-

tility is highly correlated (in excess terms) with the ERI SB

U.S. Low Volatility Maximum Deconcentration portfolio,

and the two fundamental indexes have also varied together

over time.

These statistics imply that releasing the long-only

constraint would lead to far more efficient harvesting of the

factors targeted by these strategies. Evidence suggests that

investment insights can generally be more effectively applied

when both long and short positions are allowed. The way that

we define alternative indexes, which mirrors the industry

definition, explicitly precludes short selling. The result is the

inclusion of a substantial amount of beta (market character-

istics), which masks much of the portfolio tilt. The large

difference between total and excess correlations displayed in

Exhibits A15 and A16 underlines this point.

E X H I B I T A15

Historical Excess Return Correlations

(10 years ending 12/31/2013)



ENDNOTES

The author wishes to thank Greg Allen, Ivan “Butch”

Cliff, and Jay Kloepfer for their essential contributions to the

development of this article.

1Technically the CAPM model explains excess returns

or returns above the risk-free rate (traditionally defined as the

return on 90-day T-Bills). It also includes a residual term.

This translation omits both of these components to simplify

the definition in an effort to enhance readability.

E X H I B I T A16

Historical Excess Return Correlations




2S&P Dow Jones Indexes.3Russell.4MSCI.5MSCI.6Surplus risk is the standard deviation of assets minus

liabilities.

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